Anisotropic Resistivity Size Effect in Epitaxial Mo(001) and Mo(011) Layers.

Mo(001) and Mo(011) layers with thickness = 4-400 nm are sputter-deposited onto MgO(001) and α-AlO(112¯0) substrates and their resistivity is measured in situ and ex situ at room temperature and 77 K in order to quantify the resistivity size effect. Both Mo(001) and Mo(011) layers are epitaxial single crystals and exhibit a resistivity increase with decreasing due to electron surface scattering that is well described by the classical Fuchs and Sondheimer model. Data fitting yields room temperature effective electron mean free paths 14.4 ± 0.3 and 11.7 ± 0.3 nm, respectively, indicating an anisotropy with a smaller resistivity size effect for the Mo(011) orientation. This is attributed to a smaller average Fermi velocity component perpendicular to (011) surfaces, causing less surface scattering and a suppressed resistivity size effect. First-principles electronic structure calculations in combination with Boltzmann transport simulations predict an orientation dependent transport with a more pronounced resistivity increase for Mo(001) than Mo(011). This is in agreement with the measurements, confirming the effect of the Fermi surface shape on the thin-film resistivity. The predicted anisotropy λ001*/λ011* = 1.57 is in reasonable agreement with 1.66 and 1.23 measured at 77 and 295 K. The overall results indicate that the resistivity size effect in Mo is relatively small, with a measured product of the bulk resistivity times the effective electron mean free path = (7.7 ± 0.3) and (6.2 ± 0.2) × 10 Ωm for Mo(001) and Mo(011) layers. The latter value is in excellent agreement with the first-principles-predicted 5.99 × 10 Ωm and is 10% and 40% smaller than the reported measured for Cu and W, respectively, indicating the promise of Mo as an alternate conductor for narrow interconnects.